Publication date: Jan 2008
Abstract:
We apply a genetic algorithm method for selection of neutron star models
relating them to the resonant models of the twin peak quasiperiodic
oscillations observed in the X-ray neutron star binary systems. It was
suggested that pairs of kilo-hertz peaks in the X-ray Fourier power
density spectra of some neutron stars reflect a non-linear resonance
between two modes of accretion disk oscillations. We investigate this
concept for a specific neutron star source. Each neutron star model is
characterized by the equation of state (EOS), rotation frequency Ω and
central energy density ρc . These determine the spacetime structure
governing geodesic motion and position dependent radial and vertical
epicyclic oscillations related to the stable circular geodesics.
Particular kinds of resonances (KR) between the oscillations with
epicyclic frequencies, or the frequencies derived from them, can take
place at special positions assigned ambiguously to the spacetime
structure. The pairs of resonant eigenfrequencies relevant to those
positions are therefore fully given by KR,ρc , Ω, EOS and can be
compared to the observationally determined pairs of eigenfrequencies in
order to eliminate the unsatisfactory sets (KR,ρc , Ω, EOS). For the
elimination we use the advanced genetic algorithm. Genetic algorithm
comes out from the method of natural selection when subjects with the
best adaptation to assigned conditions have most chances to survive. The
chosen genetic algorithm with sexual reproduction contains one
chromosome with restricted lifetime, uniform crossing and genes of type
3/3/5. For encryption of physical description (KR,ρ, Ω, EOS) into
chromosome we used Gray code. As a fitness function we use
correspondence between the observed and calculated pairs of
eigenfrequencies.
Authors:
Stuchlik, Zdenek; Urbanec, Martin; Török, Gabriel; Bakala, Pavel; Cermak, Petr;